Pen-drawn Marangoni swimmer

Pen-drawing is an intuitive, convenient, and creative fabrication method for delivering emergent and adaptive design to real devices. To demonstrate the application of pen-drawing to robot construction, we developed pen-drawn Marangoni swimmers that perform complex programmed tasks using a simple and accessible manufacturing process. By simply drawing on substrates using ink-based Marangoni fuel, the swimmers demonstrate advanced robotic motions such as polygon and star-shaped trajectories, and navigate through maze. The versatility of pen-drawing allows the integration of the swimmers with time-varying substrates, enabling multi-step motion tasks such as cargo delivery and return to the original place. We believe that our pen-based approach will significantly expand the potential applications of miniaturized swimming robots and provide new opportunities for simple robotic implementations.

1) The theoretical parts are quite unclear. The authors briefly show the equations 1 to 3. However, they do not clearly show what are the variable and what are the constants. Especially, in equations 1 and 2, Gamma(x,t) looks like a variable, but in equation 3 Gamma(t) is given. It makes the readers confused.
2) As for the theoretical work of the camphor particles with various shapes has been reported. The author did not cite the previous work on the theoretical framework. The followings are some of them: -Mathematical modeling and analysis M. Nagayama, S. Nakata, Y. Doi, and Y. Hayashima, A theoretical and experimental study on the unidirectional motion of a camphor disk, Physica D 194, 151 (2004).
-Review for the camphor particle motion S. Nakata, M. Nagayama, H. Kitahata, N. J. Suematsu, and T. Hasegawa, Physicochemical design and analysis of self-propelled objects that are characteristically sensitive to environments, Phys. Chem. Chem. Phys. 17, 10326 (2015) 3) In the supporting information, the authors show the mathematical model for the two-dimensional motion. I cannot totally understand the model in SI. Since the authors consider the two-dimensional motion, I think Gamma (x,t) should be Gamma(x,y,t). Thus, the expression Gamma(x,t) in equation (3) in the main text should no longer work. 4) Related to the comment 3, the force originating from the surface tension should work the whole object. I do not think this fact is not included in the model.

5)
The authors fails to cite the references that are much related to the present contents: -Translational and Rotational motion of a camphor particle S. Nakata, Y. Iguchi, S. Ose, M. Kuboyama, T. Ishii and K. Yoshikawa, Self-Rotation of a Camphor Scraping on Water: New Insight into the Old Problem, Langmuir, 1997, 13, 4454-4458. -Design of the self-propelled objects using camphor particles H. Morohashi, M. Imai, and T. Toyota, Construction of a chemical motor-movable frame assembly based on camphor grains using water-floating 3d-printed models, Chem. Phys. Lett. 721, 104 (2019) -New material for self-propulsion including polymers R. J. G. Löffler , M. M. Hanczyc and J. Gorecki, A Perfect Plastic Material for Studies on Self-Propelled Motion on the Water Surface, Molecules, 26, 3116 (2021).
Reviewer #4 (Remarks to the Author): Marangoni swimmers are designed by drawing with a pen with camphor ink. Camphor release induces surface tension gradients which, in turn, causes swimmer propulsion. The authors demonstrate swimmers that can follow complex trajectories and successfully execute multistep tasks. The idea and implementation very interesting and can inspire further design and prototyping of multifunctional swimmers. The paper is well written and organized and will be of interest to a broad readership. Several changes can be suggested before publication: 1. In Figure 2 the legend in panel d need to be arranged concentration. In the same figure, clarify what the colorbars in panels e and f represents.
2. An explain of how intermittent motion is achieved need to be included.
3. Comment on the reproducibility of the results, especially when complex trajectories are considered.
4. It will be useful to discuss miniaturization of the technology and relevant limitations.
5. Discuss what sets the overall time of the camphor release and how the release time can be regulated.

General Response
We appreciate the thoughtful comments from the reviewers based on the manuscript. We find their feedback very helpful in improving and completing our manuscript. In this letter, we address the reviewers' comments. All revised content in response to the comments is highlighted in yellow in both the Manuscript and the Supplementary Information. Text taken from the Manuscript or Supplementary Information is indicated in italics in this Response Letter.

Response to reviewer #1's comments
General Comment: The authors of this article present a series of compelling experiments on Marangoni swimmers created in an extremely versatile manner employing direct drawing of patches releasing camphor using a pen. The physics of these systems has been extensively explored and multiple applications have been already proposed. However, the simplicity and versatility of the design proposed here make this manuscript a very compelling and interesting read. Given the simplicity of the approach, I expect many to follow these steps. The visual information in the form of figures and supporting videos is extremely clear and the text is easy to follow also for non-experts. Even if the experiments and their interpretation are simple, they are carefully carried out and are supported by detailed calculations. I therefore recommend publication in Nature Communications. I only have a minor comment, which I would like the authors to consider before publication.

Comment 1:
The equations on page 6 are just placed there and are not really connected to the rest of the text. I suggest that they are moved to the SI, where the authors describe the modeling in detail.

Response for General Comment and Comment 1:
Thank you for the supportive and positive feedback on our manuscript. We have carefully addressed the minor comments related to the equations by moving them to the Supplementary Information section and providing improved descriptions to enhance reader comprehension. The relocated equations can be found highlighted in yellow in the revised Manuscript and Supplementary Information.

Manuscript
We show that the motion trajectory of a swimmer can be programmed using a drawing pattern (Fig. 2e and Supplementary Movie 3). We tested three different patterns: two camphor-ink dots on the vehicle but with different arrangements. Depending on the location of the dots (i.e., pattern of camphor-ink drawing), the swimmers have different trajectories, such as linear, circular, or rotational motion. The trajectory of the Marangoni swimmer can be mathematically modeled by calculating the driving force generated due to camphor release and assuming that the force acts on the camphor-ink-drawn area (referred to as the camphor engine hereinafter) (See Supplementary Text) 30,[37][38][39] . However, due to the complexity of factoring in the swimmer's shape and the camphor engine design, we opted to implement this estimation through the finite element analysis (FEA) simulation (Fig. 2e) (see Supplementary Text).

Mathematical modeling and FEA simulation for predicting camphor-driven swimmer trajectories
The first term on the right-hand side depicted surface diffusion of camphor molecules. The second term means the sublimation (from the water surface to the air) and dissolution (from water surface to the bulk water phase) of the camphor molecules. The last term is the supply of the camphor molecules from the camphor engine, where ( , ) is described as 0 in the region in two-dimensional space that corresponds to the shape of the camphor engine, and 0 in the other region. We presume a linear relation between γ and for simplicity. (γ is a surface tension.) Above equations (2) and (3) (7).
Reaction-diffusion equation: where the delta function, , denotes the assumption that the camphor molecules are supplied only to the stern of the boat 9 .
Newtonian equation:  (5) can be reasonably approximated and solved as equation (8), where m is the mass of the boat (0.07 g) and is the initial velocity of the swimmer.
Then the value of μ (3.327 10 −5 Nm −1 s) can be derived from the slope of ( ). Subsequently, we calculated the driving force 0 of each camphor engine of different concentrations from their steady-state velocity using the following equation (7).
Because the constants k and D are broadly applicable to a variety of situations regardless of the shape of the swimmer, we used the values k = 2 10 −2 s −1 and D = 4 10 −3 m 2 s −1 adopted from a previous report (N. J. Suematsu et al., Langmuir 2014)  Thank you again for your feedback and for considering our manuscript for publication in Nature Communications.

Response to reviewer #2's comments
General Comment: The authors describe a technique for producing Marangoni swimmers and other objects that generate Marangoni flows. The technique is based on loading a marker pen with ink that contains camphor. Using the pen to write on otherwise generic objects patterns them with local stores of camphor that are gradually released and cause Marangoni flows when the surface contacts water. The authors demonstrate this with pieces of PET film, acrylic, paper, leaves, and 3D printed structures. Moreover, the authors demonstrate that such Marangoni swimmers can be designed to move linearly, spin around, or perform more complex manoeuvres, such as following a maze-like confined path by combining a pattern that generates forward propulsion with a pattern that causes side-to-side oscillations.
To add further complexity, the authors used folded paper, which gradually unfolds upon contact with water to expose different patterns to the water. Different conformations of the structure could be associated with different Marangoni-driven motion.
The novelty in this work is the pen-drawing technique of patterning objects for Marangoni flow. This is significant because it allows very quick and convenient production of swimmers with different patterns, which could facilitate further detailed studies.
The authors have shown a good variety of examples from simple to complex, time-dependent behaviours. In my opinion, the work is of good quality and sufficiently impactful to warrant consideration for publication in Nature Communications. The manuscript is clearly written and figures are well made. Experimental procedures appear to be sound and adequately described, but this aspect is beyond my expertise.

Response for General Comment:
We are grateful for the reviewer's time and expertise to carefully reviewing our work and for the insightful comment. We sincerely apologize for any misunderstandings or unintentional misleadings that have arisen regarding the theoretical analysis and simulation part. Thanks to the reviewer's comment, we could be aware of the critical flaws that we have stated in the previous manuscript. We appreciate the opportunity to address these concerns and improve our manuscript, ensuring the clarity and accuracy of our work.

Comment 1:
The theoretical modeling and simulation results, however, were somewhat unclear and weak. From the descriptions in the main text and supplementary text, the friction coefficient mu and the driving force are inputs for the finite element analysis. It is not clear what the purpose of the FEA is, then. Mechanical properties of the material are quoted, so presumably strains are calculated but they are not discussed at all in the text. It seems that FEA was only used to calculate trajectories of the swimmers but this approach is not necessary if one already has a formula for the driving force. One can directly solve the equations of motion (2) and (4).

Response 1:
We appreciate your observation that the purpose of the FEA in our study might have been unclearly described in the previous manuscript. As pointed out, our initial aim was to predict the trajectories of the swimmers using FEA. It is true that trajectories of various swimmers can be calculated using theoretical modeling performed by other researchers, but such calculations can be relatively complex to be applied in every swimmer with diverse design. Therefore, we attempted to simplify the prediction of the trajectories by employing a simplified linear model (1-dimensional model) to compute the driving force of various concentrations of camphor ink and applying these forces locally to the spot of the swimmer where the engines are drawn (2-dimensional model). We acknowledge that this might not have been clearly conveyed in the previous manuscript, and we have revised it accordingly to better articulate our approach and its rationale. Based on another reviewer's comment, we have moved all the theoretical modeling equations to the Supplementary Information, rather than partially explaining them in the Manuscript.

Manuscript
We show that the motion trajectory of a swimmer can be programmed using a drawing pattern ( Fig. 2e   Predicting an object's trajectory can be achieved through a comprehensive analysis of the net force and net torque applied to the object. By understanding these factors, it becomes possible to anticipate the motion and behavior of the Marangoni swimmer in various situations.

Mathematical modeling and FEA simulation for predicting camphor-driven swimmer trajectories
For example, let's consider a rectangular Marangoni swimmer with two camphor engines placed on one edge, as shown below.
We refer to the two-dimensional modeling of a Marangoni swimmer's motion studied by H. Kitahata and colleagues 1 . The surface concentration of camphor molecules is defined as ( , , ), which is represented as for simple notation in equation (1). To figure out the trajectories of the swimmer derived by the camphor molecules in two-dimensional space, we need to consider three equations: reaction-diffusion equation for camphor molecules, net force equation, and net torque equation exerted on the swimmer.
The first term on the right-hand side depicted surface diffusion of camphor molecules. The second term means the sublimation (from the water surface to the air) and dissolution (from water surface to the bulk water phase) of the camphor molecules. The last term is the supply of the camphor molecules from the camphor engine, where ( , ) is described as 0 in the region in two-dimensional space that corresponds to the shape of the camphor engine, and 0 in the other region. We presume a linear relation between γ and for simplicity. (γ is a surface tension.) Above equations (2) and (3) (7).

Reaction-diffusion equation:
where the delta function, , denotes the assumption that the camphor molecules are supplied only to the stern of the boat 9 .
Newtonian equation:  (5) can be reasonably approximated and solved as equation (8), where m is the mass of the boat (0.07 g) and is the initial velocity of the swimmer.
Then the value of μ (3.327 10 −5 Nm −1 s) can be derived from the slope of ( ). Subsequently, we calculated the driving force 0 of each camphor engine of different concentrations from their steady-state velocity using the following equation (7).
Because the constants k and D are broadly applicable to a variety of situations regardless of the shape of the swimmer, we used the values k = 2 10 −2 s −1 and D = 4 10 −3 m 2 s −1 adopted from a previous report (N. J. Suematsu et al., Langmuir 2014)  We hope that these revisions address your concerns and appreciate your guidance in improving our manuscript.

Comment 2:
The principles that are demonstrated in this work are interesting but there is scope for better quantitative modeling of the motions produced by different patterns. The theoretical analysis in the supplementary text attempts to address this but appears to have some significant flaws. For instance, it is assumed that the direction of the forces at the patterned corners is vertical (as shown in the supplementary figure) but no explanation is given for this. Moreover, in the process of deriving the magnitude of these forces, it is stated that (i) the spatial gradient of camphor is negligible and that (ii) the concentration of released camphor molecules is negligible. Each of these assumptions should mean that the surface tension is the same everywhere, i.e., there is no Marangoni flow and no motion of the swimmer. Even with the presentation clarified, the basis of this model is the formula for the force proposed in Ref 27, which was based on linear motion and therefore had an unambiguous direction even if details of the (symmetric) shape were omitted. For rotational motion, the direction of the forces each ink patch produces must depend on the shape of the swimmer.

Response 2:
We acknowledge that there were significant mistakes in our model, and we apologize for any confusion this may have caused. We appreciate the opportunity to correct these errors and ensure the accuracy of our work. Thanks to the reviewer's feedback, we have become aware of the critical flaws in theoretical analysis, which we had previously misunderstood. Reviewer's guidance has been invaluable in helping us identify the areas that require revision and improvement. As a result, we have revisited and revised the entire theoretical analysis section to address the issues the reviewer raised, as described in Response 1.
To address the particular issues that you have raised in Comment 2, please find our detailed responses below: 1) For instance, it is assumed that the direction of the forces at the patterned corners is vertical (as shown in the supplementary figure) but no explanation is given for this.
In response to the comment regarding the assumption that the direction of the forces at the patterned corners is vertical, we apologize for any confusion our initial explanation may have caused. We changed the example to explain the trajectory of the swimmer as shown below For example, let's consider a rectangular Marangoni swimmer with two camphor engines placed on one edge, as shown below.
Above equations (2) and (3)  Additionally, we would like to emphasize that both vertical and horizontal forces are included in our FEA simulations. We have revised the simulation section of our manuscript to highlight this aspect. We believe that this revised approach provides a more accurate representation of the forces at the patterned corners and is better suited for our system. Thank you for bringing this important matter to our attention.
For the camphor inks applied in dots, we analyzed the diameter of the dots (~ 2.5 mm) and applied the driving pressure to the nearest side of the swimmer with equal length. For the dots located in the vertex, the driving pressure was applied to both nearest sides of the swimmer.
2) Moreover, in the process of deriving the magnitude of these forces, it is stated that (i) the spatial gradient of camphor is negligible and that (ii) the concentration of released camphor molecules is negligible. Each of these assumptions should mean that the surface tension is the same everywhere, i.e., there is no Marangoni flow and no motion of the swimmer.
We apologize for the oversight and have since revised our theoretical modeling to address these issues. The updated modeling now provides a more accurate representation of the Marangoni flow and the motion of the swimmer. Please find the revised theoretical modeling and corresponding discussions in the updated manuscript.  (7).

Reaction-diffusion equation:
where the delta function, , denotes the assumption that the camphor molecules are supplied only to the stern of the boat 9 .
Newtonian equation: We are grateful for your valuable feedback, which has helped us identify and correct this crucial error, and we hope that our revised modeling now adequately addresses your concerns.
3) Even with the presentation clarified, the basis of this model is the formula for the force proposed in Ref 27, which was based on linear motion and therefore had an unambiguous direction even if details of the (symmetric) shape were omitted. For rotational motion, the direction of the forces each ink patch produces must depend on the shape of the swimmer.
We understand your concern about the applicability of this formula to rotational motion, given that it was originally derived for linear motion with an unambiguous direction. In our study, we utilized the formula for linear motion to calculate the driving force in a simplified manner, and assumed that the force is acting locally on the camphor engine using FEA simulation. We acknowledge that this approach may not fully capture the complex dynamics required to precisely estimate the trajectory of the swimmer. However, it does allow us to easily predict the swimmer's trajectory while considering the swimmer's shape, without the need to solve complex equations.
We have included a detailed explanation of our methodology, as well as the limitations of our current approach, in both the manuscript and the supplementary information.
Additionally, we have referenced other research that has more accurately calculated the motion of similar systems. This context helps to highlight the trade-offs made in our study for the sake of simplicity, and provides a foundation for potential improvements in future work. We believe that these changes will significantly enhance the quality and rigor of our work, providing a more comprehensive understanding of the principles governing the motion of Marangoni swimmers with different patterns.

Comment 3:
In equation 2 of the main text and equation 3 of the supplementary material, r and r_0 should be gamma and gamma_0, respectively. Also, in the supplementary text, equations 6-7 have missed the parentheses around Gamma(x,t), making it look like a product of gamma and Gamma whereas actually Gamma is the argument of gamma.

Response 3:
We would like to extend our sincere apologies for any typos present in the manuscript. We understand that such errors can make it difficult to read and comprehend the content, especially in the equation part, and we deeply regret any inconvenience this may have caused during the review process. We carefully proofread the manuscript and corrected all typos. We appreciate the reviewer for the understanding and thank once again for the valuable feedback.
Comment 4: "The mean surface concentration can be derived using equation (3)… This implies that Marangoni propulsion, which is the difference in the surface tension around the vehicle, increases when the release ratio of the camphor molecules increases." It is reasonable that the propulsion increases when the release ratio increases but this is not related to equation (3), which only describes the mean concentration (which does not contribute to Marangoni propulsion).

Response 4:
We would like to reiterate our appreciation for your insightful feedback, which has been crucial in helping us identify and address the critical flaws in our theoretical analysis. Your guidance has played a pivotal role in our understanding of the issues at hand, allowing us to significantly improve our work. By revising the entire theoretical analysis section, we have been able to correct our previous misunderstandings and ensure the accuracy of our research. We would like to kindly inform the reviewer that we have carefully addressed the concerns raised in the following manner:  (7).

Reaction-diffusion equation:
where the delta function, , denotes the assumption that the camphor molecules are supplied only to the stern of the boat 9 .
Newtonian equation: We are truly grateful for your valuable input and believe that, thanks to your comments, our manuscript has been greatly strengthened.
Comment 5: Variables in the equations should be defined. Also, the mean surface concentration in equation (3) should be distinguished from the spatially-dependent variable, e.g., with a bar above the Gamma symbol.
Response 5: We sincerely apologize for misleadings that the previous equations have caused.
We have thoroughly revisited the theoretical part of our study and have revised the issues raised in comment 5. Also, we defined all the variables in the theoretical remodeling part as follows. Comment 6: Details of the FEA were missing, such as shape and dimensions of the 3D object. What direction is the driving pressure applied for the dots? Following figures in the manuscript, the dots should be placed on the horizontal surfaces so pressure would act vertically and not drive horizontal motion.

Response 6:
We appreciate your attention to the details of the finite element analysis (FEA) and concern regarding the shape, dimensions, and driving pressure direction of the 3D object.
We understand that providing these details is important for a clear understanding of our methodology. In response to this comment, we have added the necessary information regarding the simulation in Supplementary Information as follows.  (5) can be reasonably approximated and solved as equation (8), where m is the mass of the boat (0.07 g) and is the initial velocity of the swimmer.
Then the value of μ (3.327 10 −5 Nm −1 s) can be derived from the slope of ( ). Subsequently, we calculated the driving force 0 of each camphor engine of different concentrations from their steady-state velocity using the following equation (7).
Because the constants k and D are broadly applicable to a variety of situations regardless of the shape of the swimmer, we used the values k = 2 10 −2 s −1 and D = 4 10 −3 m 2 s −1 adopted from a previous report ( where cs is the fitted coefficient (cs = 1.4 kg/m 3 ) from the circular trajectory in Fig. 2e, n is the normal unit outward from the element where the surface pressure is applied, and vref is the velocity of the reference node.
In all simulations, the swimmers with length = 20 mm, width = 10 mm, and height = 0.3 mm were constructed with 3D deformable solid elements of type C3D8 using a linear elastic model. The mechanical properties were determined by using the following input parameters: density d = 1.45 g/cm 3 , Young's modulus E = 3.275 GPa, and Poisson's ratio v = 0.4.
Comment 7: "We demonstrated a square-shaped trajectory by selecting the optimal concentration of the camphor ink (Fig 3b, right)." This suggests that the camphor concentration is the main parameter that needs to be tuned but it must surely also be somewhat sensitive to how the pattern is drawn, e.g., thickness and lengths of lines, radius of dots. More generally, could the authors comment on how reproducible the behavior of swimmers was? Is it possible to reliably make swimmers with the same motion? Closed, periodic trajectories such as the square and star-shaped paths should be especially difficult to control accurately.
Response 7: Thank you for your comment regarding the reproducibility of our work. We have added some more experimental data ( Supplementary Fig. 3) to demonstrate the reproducibility of complex motion programming and believe that this will further improve the quality of this manuscript.
In our first demonstration of complex motion programming, the star-shaped trajectory, we observed fairly consistent moving modalities across multiple trials. The swimmers consistently traveled along the boundary while bouncing off walls. Out of five additional attempts, all succeeded in obtaining a similar moving trajectory. However, the angle between vertices, influenced by the balance between oscillation moving speed and rotation speed, varied among trials. Two out of the five trials resulted in a 4-pointed star-shaped trajectory. We acknowledge that this variability may stem from the intrinsic sensitivity of manual hand drawing (e.g., thickness and lengths of lines, radius of dots), as the reviewer have pointed out. We anticipate that the accuracy can be improved if we adopt a more accurate fabrication method, such as inkjet based printing or lithography.
Our second demonstration, the polygonal trajectory, also displayed high reproducibility, with all five attempts resulting in successful trials. However, similar to the star-shaped trajectory, the rotation angle at each vertex varied among trials, leading one of the five attempts to produce a hexagonal trajectory instead of a square trajectory. We attribute this variation to the inaccuracy caused by manual hand drawing. To better convey our findings, we have opted to use the term "polygonal trajectory" rather than "square trajectory." To enhance the clarity of our manuscript, we have included additional explanations and experimental data in the main text and Supplementary materials, addressing the concerns you raised.

Manuscript
We investigated the reproducibility of these complex motion programming, as shown in Supplementary Fig. 3. First, for the programming of the star-shaped trajectory, all five attempts from the five trials were successful in drawing star-shaped trajectories that traveled along the boundary while bouncing off a wall (Supplementary Fig. 3a). However, there were some differences in the angle between each vertex depending on the attempt, which seems to be due to the inaccuracy caused by manual hand drawing. Three out of five attempts showed a five-pointed star shape, and the other two had approximately a four-pointed star shape. Secondly, the reproducibility of the polygonal trajectory was investigated as shown in Supplementary Fig. 3b. Every experiment from five attempts showed a polygonal trajectory with periodic movement, but one of them had a lack of rotation angle in the vertex, which led to a hexagonal path, rather than a square path like the others. We believe that this inaccuracy can be improved if we adopt a more precise printing method rather than manual hand drawing. Supplementary Fig. 3. Reproducibility of complex motion programming.  Response 8: Thank you for your thoughtful comment and inquiry into the potential effects of the water-soluble bridge on the Marangoni fuel propulsion. We appreciate the opportunity to provide further clarification on this matter.

Supplementary Information
We acknowledge that the pullulan film could potentially act as a Marangoni fuel by reducing the surface tension of water as it dissolves. To minimize any undesired effects on the swimmer's trajectory, we carefully designed the bridging films with the following considerations: Firstly, the pullulan films were designed to be bilaterally symmetrical around the direction of progress before disassembly. Thus, the pullulan film does not exert net force in the direction vertical to the heading direction. Secondly, the dissolvable area is not exposed to the front or back parts of the vehicle, minimizing any forward or backward propulsion force generated by the pullulan film before disassembly. The dissolved pullulan molecules primarily diffuse into the bulk water phase underneath the vehicle (Fig. 7a) or underneath the vehicle and symmetrically to the side (Fig. 7b), which has little effect on the swimmer's movement. In fact, the modeling of Marangoni swimmer movement often overlooks the dissolution of molecules into the bulk water phase (N. J. Suematsu et al., Langmuir 2014). Additionally, considering the swimmer's forward movement shown in Fig. 7 before disassembly, we can identify that the bridging film does not generate any unwanted backward propulsion force, which can overcome the propulsion force generated by the camphor engine.
We agree that incorporating this explanation into the manuscript will enhance readers' understanding of the study. Accordingly, we have updated the manuscript (Highlighted in yellow) to include this information.
After the subsidence of the instant boost in motion due to the water-soluble film, the individual swimmers followed the designated locomotion according to their camphor engine design and vehicle shape. Since the bridging film can decrease the surface tension of water as it dissolves and potentially acts as a Marangoni fuel, the location of the bridging films needs to be carefully designed to avoid any unwanted directional changes before disassembly. To achieve this, we designed the pullulan films to be bilaterally symmetrical around the heading direction and to not be exposed to the front or back of the vehicle. This ensures that no rotational, forward or backward propulsion force is generated by the bridging film before disassembly.

General Comment:
The paper reports on a new experimental system on "Marangoni swimmer". A material that releases surface active chemicals to the surrounding water surface is known to exhibit self propulsion. Camphor is one of the most famous chemicals for such motion. When a camphor particle is put on the water surface, it moves spontaneously since surface tension around the particle decreases due to the camphor molecules and the surface tension working on the particle becomes unbalanced. The authors newly designed the material that shows the self-propulsion. The advantage of the material is the ease in molding. The authors claim that they can make the swimmer like "pen-writing". Then, they have shown many examples on the interesting behaviors using the new material. The development of the material is novel and important, and therefore I think the manuscript has a potential to be published in Nature Communications. However, each result shown in the figures and movies has been reported using the other systems. Thus, the authors have to comment on the previous related results. Moreover, the theoretical and numerical parts are poorly written. The manuscript should be reviewed again after the author revises based on the comments.

Response for General Comment:
We appreciate the acknowledgement of the novelty and importance of our pen-drawn Marangoni swimmers. We thoroughly reviewed the relevant literature and updated all referred articles that the reviewer has suggested. We also apologize for any shortcomings in the presentation of the theoretical and numerical parts of the manuscript. We are grateful for the opportunity to address these concerns and improve our manuscript. Response 1: We apologize for the confusion caused by the presentation of the theoretical parts and the lack of clarity regarding the variables and constants in the equations. We understand that our previous explanation may have been unclear and misleading. We have thoroughly revisited the theoretical analysis part, and revised the manuscript and supplementary information to provide a comprehensive explanation of the Marangoni propulsion. In our study, we employed a formula for linear motion to calculate the driving force in a simplified manner, and assumed that the force acts locally at the spot where the engine is drawn to predict the trajectory of the swimmer in 2-dimensional space using FEA simulation. Based on another reviewer's comment, we have moved all the theoretical modeling equations to the Supplementary Information, rather than partially explaining them in the Manuscript. Followings are the modified parts of Manuscript and Supplementary Information regarding the theoretical parts and the simulation part.

Manuscript
We show that the motion trajectory of a swimmer can be programmed using a drawing pattern ( Fig. 2e and 30,[37][38][39] . However, due to the complexity of factoring in the swimmer's shape and the camphor engine design, we opted to implement this estimation through the finite element analysis (FEA) simulation (Fig. 2e) (see Supplementary  Text). Predicting an object's trajectory can be achieved through a comprehensive analysis of the net force and net torque applied to the object. By understanding these factors, it becomes possible to anticipate the motion and behavior of the Marangoni swimmer in various situations.

Mathematical modeling and FEA simulation for predicting camphor-driven swimmer trajectories
For example, let's consider a rectangular Marangoni swimmer with two camphor engines placed on one edge, as shown below.
We refer to the two-dimensional modeling of a Marangoni swimmer's motion studied by H. Kitahata and colleagues 1 . The surface concentration of camphor molecules is defined as ( , , ), which is represented as for simple notation in equation (1). To figure out the trajectories of the swimmer derived by the camphor molecules in two-dimensional space, we need to consider three equations: reaction-diffusion equation for camphor molecules, net force equation, and net torque equation exerted on the swimmer.
The first term on the right-hand side depicted surface diffusion of camphor molecules. The second term means the sublimation (from the water surface to the air) and dissolution (from water surface to the bulk water phase) of the camphor molecules. The last term is the supply of the camphor molecules from the camphor engine, where ( , ) is described as 0 in the region in two-dimensional space that corresponds to the shape of the camphor engine, and 0 in the other region. We presume a linear relation between γ and for simplicity. (γ is a surface tension.) Above equations (2) and (3) (7).

Reaction-diffusion equation:
where the delta function, , denotes the assumption that the camphor molecules are supplied only to the stern of the boat 9 .
Newtonian equation:  (5) can be reasonably approximated and solved as equation (8), where m is the mass of the boat (0.07 g) and is the initial velocity of the swimmer.
Then the value of μ (3.327 10 −5 Nm −1 s) can be derived from the slope of ( ). Subsequently, we calculated the driving force 0 of each camphor engine of different concentrations from their steady-state velocity using the following equation (7).
Because the constants k and D are broadly applicable to a variety of situations regardless of the shape of the swimmer, we used the values k = 2 10 −2 s −1 and D = 4 10 −3 m 2 s −1 adopted from a previous report (N. J. Suematsu et al., Langmuir 2014)  We hope that these revisions address the your concerns and appreciate the guidance in improving our manuscript.
Comment 2: As for the theoretical work of camphor particles with various shapes has been reported. The author did not cite the previous work on the theoretical framework. The followings are some of them: -Mathematical modeling and analysis M. Nagayama et al., Physica D 194, 151 (2004).

Response 2:
We appreciate the reviewer for pointing out the omission of previous theoretical works on camphor particles with various shapes. We understand the importance of acknowledging and building upon the existing literature in our research. In response to this comment, we have carefully reviewed the provided references, as well as conducted additional literature searches to identify other relevant works. We have now cited and discussed these previous theoretical studies in the revised manuscript to give appropriate credit and to contextualize our work within the broader research landscape. We believe that incorporating these references and discussions will strengthen the theoretical framework of our study and provide a more comprehensive understanding of the subject matter. We apologize for any oversight on our part and are grateful for the reviewer's guidance in helping us to improve our manuscript. Followings are the parts of the Manuscript that cite abovementioned references.
The trajectory of the Marangoni swimmer can be mathematically modeled by calculating the driving force generated due to camphor release and assuming that the force acts on the camphor-ink-drawn area (referred to as the camphor engine hereinafter) (See Supplementary  Text) 30,[37][38][39] .

Comment 3 and 4:
In the supporting information, the authors show the mathematical model for the two-dimensional motion. I cannot totally understand the model in SI. Since the authors consider the two-dimensional motion, I think Gamma (x,t) should be Gamma(x,y,t). Thus, the expression Gamma(x,t) in equation (3) in the main text should no longer work. Related to the comment 3, the force originating from the surface tension should work the whole object. I do not think this fact is not included in the model.

Response 3 and 4:
We appreciate your comments and understand that our mathematical model for the two-dimensional motion may have been unclear. Initially, our approach was to calculate the driving force from the simplified linear equations (1-dimensional model), and apply the driving force to the local spots where engines are drawn using the FEA simulation (2dimensional simulation). We tried to show one example of how a trajectory can be calculated using a theoretical model in the supporting information. However, in our previous manuscript, we inadvertently used one-dimensional equations of motion to describe the trajectory of a twodimensional object, which led to confusion.
We acknowledge this critical mistake and greatly apologize for any confusion that our previous equation has made. We have now clarified the equations to calculate the trajectory of the swimmer and have made the necessary corrections in the manuscript and supplementary information. The detailed corrections are as described in Response 1. Response 5: Thank you for your comment regarding the references. We apologize for not including the reference in the previous manuscript. We have now carefully reviewed the literatures and updated our manuscript to include the references as highlighted in yellow. We appreciate your feedback and believe that the updated references will enhance the quality of our work. Followings are the parts of the manuscript that we have included abovementioned references. Several studies have investigated swimmers with similar trajectories 40,41 ; however, to the best of our knowledge, a design methodology based on this modular assembly concept has not yet been reported.

Response to reviewer #4's comments
General Comment: Marangoni swimmers are designed by drawing with a pen with camphor ink. Camphor release induces surface tension gradients which, in turn, causes swimmer propulsion. The authors demonstrate swimmers that can follow complex trajectories and successfully execute multistep tasks. The idea and implementation are very interesting and can inspire further design and prototyping of multifunctional swimmers. The paper is well written and organized and will be of interest to a broad readership. Several changes can be suggested before publication: Response for General Comment: We thank the reviewer for their positive assessment of our work on Marangoni swimmers. We are pleased to hear that our demonstration of the ability of the swimmers to follow complex trajectories and execute multistep tasks was interesting and inspiring. We also appreciate the reviewer's recognition of the potential of this work to contribute to the design and prototyping of multifunctional swimmers.
We have carefully considered the changes suggested by the reviewer and incorporated them into our revised manuscript. Once again, we appreciate the reviewer's valuable feedback and are grateful for their time and effort in reviewing our manuscript.
Comment 1: In Figure 2 the legend in panel d need to be arranged concentration. In the same figure, clarify what the colorbars in panels e and f represents. Comment 2: An explanation of how intermittent motion is achieved needs to be included.

Fig. 2. Controllable motion of pen-drawn Marangoni swimmers. a-c
Response 2: Thank you for your comment. We agree that an explanation of how intermittent motion is achieved is necessary and have included our theoretical model in Supplementary Fig.  2. However, we acknowledge that the visibility of this Supplementary Figure in the current version of the manuscript may be limited. Therefore, we have modified the manuscript to make it clearer, by referring to Supplementary Fig. 2 in the main text and providing a more visible quotation of the figure as below. We hope this addresses your concern, and we appreciate your feedback.
The periodic motion of camphor swimmers has been investigated in previous studies 42,44,45 . Similarly, we implemented the periodic movement of a pen-drawn Marangoni swimmer by creating an asymmetric design using camphor inks of two different concentrations (Fig. 3b,  left). Our theoretical model of this periodic movement is shown in Supplementary Fig. 2.
Comment 3: Comment on the reproducibility of the results, especially when complex trajectories are considered.
Response 3: To address the reviewer's comment, we conducted additional experiments to investigate the reproducibility of the complex motion programming.
The first demonstration of complex motion programming, the star-shaped trajectory, is fairly reproducible in terms of its moving modality, which travels along the boundary while bouncing off a wall. We attempted the programming five more times, and all of the attempts succeeded in obtaining such a moving trajectory. However, the angle between vertices, which is affected by the balance between oscillation moving speed and rotation speed, was not 100% reproducible, and two out of five trials showed a 4-pointed star-shaped trajectory. We consider that this is due to the sensitivity that depends on how the pattern is drawn (e.g., thickness and lengths of lines, radius of dots), as pointed out by the reviewer, which is an intrinsic weakness of the manual hand drawing-based fabrication. We believe that this accuracy can be improved if we adopt a more accurate fabrication method, such as ink-jet based printing or lithography.
The second demonstration, the polygonal trajectory, was also highly reproducible with five successful trials out of five attempts. However, similar to the above star-shaped trajectory, the rotation angle at each vertex was not 100% reproducible, thus one of the five attempts showed a hexagonal trajectory rather than a square trajectory. We believe that this is also due to the inaccuracy caused by manual hand drawing. To be precise, we used the term "polygonal trajectory" rather than "square trajectory." To improve the reader's understanding, we have added more explanation in the manuscript and additional experimental data in the Supplementary Information as follows:

Manuscript
We investigated the reproducibility of these complex motion programming, as shown in Supplementary Fig. 3. First, for the programming of the star-shaped trajectory, all five attempts from the five trials were successful in drawing star-shaped trajectories that traveled along the boundary while bouncing off a wall (Supplementary Fig. 3a). However, there were some differences in the angle between each vertex depending on the attempt, which seems to be due to the inaccuracy caused by manual hand drawing. Three out of five attempts showed a five-pointed star shape, and the other two had approximately a four-pointed star shape. Secondly, the reproducibility of the polygonal trajectory was investigated as shown in Supplementary Fig. 3b. Every experiment from five attempts showed a polygonal trajectory with periodic movement, but one of them had a lack of rotation angle in the vertex, which led to a hexagonal path, rather than a square path like the others. We believe that this inaccuracy can be improved if we adopt a more precise printing method rather than manual hand drawing. Comment 4: It will be useful to discuss miniaturization of the technology and relevant limitations.

Supplementary
Response 4: Thank you for your comment. We agree that the discussion regarding miniaturization can be helpful to provide more information for authors.
Marangoni propulsion has previously been demonstrated as applicable for microswimmers in our prior work (Choi et al., Nat. Comm. 2021) and by others (Pena-Francesch et al., Nat. Comm. 2019). However, to miniaturize the Marangoni swimmer for use at the microscale, a microfabrication method such as photolithography is required to precisely pattern the Marangoni fuel on the vehicle, which potentially increases the difficulty of fabrication.
The pen-based fabrication we demonstrated in this study has two major advantages. The first is the convenience of the fabrication process from the hand drawing method, while the second is the ink-based printing, which makes it easy to process multiple inks of different concentrations on the same substrate, providing advanced programmability. The second advantage is applicable to general ink-based printing methods such as inkjet printing, not only to manual hand drawing. Although inkjet printing is less accessible and convenient than manual hand drawing, it can offer more precise fabrication and greater potential for miniaturization while retaining the advantage of the availability to process multiple inks with different concentrations.
In summary, while this study focused on the hand drawing method for its extreme accessibility, the concept of ink-based printing of Marangoni fuel proposed in this study has applicability for more precise and miniaturized fabrication of Marangoni swimmers combined with computeraided printing method. We have added this discussion to the manuscript as follows.

Manuscript -Discussion
Although the proposed hand drawing-based method offers exceptionally straightforward and highly accessible fabrication of Marangoni swimmers, the manual use of pen may limit the accuracy, reproducibility, and availability for miniaturization. However, the advantage of the proposed method is not just the ease of use. The ink-based printing method provides the advantage of making it easy to process different concentrations of fuel ink together on the same substrate. This enables highly advanced motion programmability. Furthermore, the ink-based fabrication of Marangoni swimmers is still compatible with conventional 2D printing technologies, such as pen-plotter and inkjet printing 9 . Combined with computer-aided design (CAD) and automated printing, more accurate, miniaturized, and mass-producible fabrication is achievable.

Comment 5:
Discuss what sets the overall time of the camphor release and how the release time can be regulated.

Response 5:
We appreciate your interest in the technical details of our work, and we would be happy to provide more information to clarify this aspect of our study.
From the previous studies regarding Marangoni swimmers, it has revealed that the overall time of the fuel release depends on many factors, including initial fuel loading amount (